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Question 855307: If 80 men dug 4 holes in 12 months, how many men would be required to dig 6 holes in 4 month?
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! If 80 men dug 4 holes in 12 months, how many men would be required to dig 6 holes in 4 month?
80 men dug 4 holes in 12 months.
divide that by 12 and you get 80 men dug 1/3 of a hole in 1 month.
divide that by 80 and you get 1 man dug 1/240 of a hole in one month.
does this make sense?
let's see.
1 man digs 1/240 of a hole in one month.
working at the same rate, that same man can dig 12/240 of a hole in 12 months.
80 men, working at the same rate per man, can dig (12 * 80) / 240 of a hole in 12 months.
(12 * 80) / 240 = 960 / 12 = 4, so:
80 men, working at the same rate per man, can dig 4 holes in 12 months.
formula makes sense, so we'll use it.
the formula can be condensed to:
rate of work that each man produces * number of men * time = units of work produced.
this can be abbreviated to r * n * t = u
r = rate of work that each man produces.
n = number of men.
t = time.
u = units of work produced.
time for this problem is in months.
units of work produced are the holes in the ground.
we start with the first statement in the problem:
80 men dug 4 holes in 12 months.
the units of work produced is 4 holes
the rate of work for each man is unknown so we'll keep it at r
the number of men is given as 80.
the time they took to do the work is given as 12 months.
the formula of r * n * t = u becomes:
r * 80 * 12 = 4
solve for r to get:
r = 4 / (80 * 12) = 4/960 = 1/240.
so far we have:
r = 1/240
n = 80
t = 12
u = 4
to confirm we did this correctly, we check the original equation out with those numbers to see if the equation is true.
we get:
r * n * t = u becomes:
1/240 * 80 * 12 = 4
simplifying this equation, we get:
240 = 240 which is true indicating we did this part of the problem correctly.
this part of the problem found the value of r which we will use in the next part of the problem.
we now look at the second part of the problem.
that part is the question:
how many men would be required to dig 6 holes in 4 months.
the basic formula is the same.
r * n * t = u
r = 1/240 that we solved for earlier (the rate that each person works is assumed to be the same).
n = n because we don't know what this is at the present time.
t = 4 months
u = 6 holes
we plug these values into the equation to get:
1/240 * n * 4 = 6
we solve for n to get:
n = 6 / (1/240 * 4) which becomes n = 6 / (4/240) which becomes n = 6 * 240/4 which becomes n = 6 * 60 which becomes 360.
if we did this correctly, then it would take 360 men to fill 6 holes in 4 months.
we confirm whether this is true or not by replacing n with 360 in the original equation to get:
1/240 * n * 4 = 6 becomes:
1/240 * 360 * 4 = 6
we simplify to get:
6 = 6 confirming that our calculation of the number of people required is good.
the answer is that it would require 360 men to fill 6 holes in 4 months.
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